1. Comput Biol Med. 2020 Apr;119:103695. doi: 10.1016/j.compbiomed.2020.103695. 
Epub 2020 Mar 5.

A partition-based optimization model and its performance benchmark for 
Generative Anatomy Modeling Language.

Demirel D(1), Cetinsaya B(2), Halic T(3), Kockara S(4), Reiners D(2), Ahmadi 
S(5), Arikatla S(6).

Author information:
(1)Department of Computer Science, Florida Polytechnic University, Lakeland, FL, 
USA.
(2)Department of Computer Science, University of Central Florida, Orlando, FL, 
USA.
(3)Department of Computer Science, University of Central Arkansas, Conway, AR, 
USA. Electronic address: tanselh@uca.edu.
(4)Department of Computer Science, University of Central Arkansas, Conway, AR, 
USA.
(5)Department of Orthopedic Surgery, University of Arkansas for Medical 
Sciences, Little Rock, AR, USA.
(6)Kitware Inc., Carrboro, NC, USA.

BACKGROUND: This paper presents a novel iterative approach and rigorous accuracy 
testing for geometry modeling language - a Partition-based Optimization Model 
for Generative Anatomy Modeling Language (POM-GAML). POM-GAML is designed to 
model and create anatomical structures and their variations by satisfying any 
imposed geometric constraints using a non-linear optimization model. Model 
partitioning of POM-GAML creates smaller sub-problems of the original model to 
reduce the exponential execution time required to solve the constraints in 
linear time with a manageable error.
METHOD: We analyzed our model concerning the iterative approach and graph 
parameters for different constraint hierarchies. The iteration was used to 
reduce the error for partitions and solve smaller sub-problems generated by 
various clustering/community detection algorithms. We empirically tested our 
model with eleven graph parameters. Graphs for each parameter with increasing 
constraint sets were generated to evaluate the accuracy of our method.
RESULTS: The average decrease in normalized error with respect to the original 
problem using cluster/community detection algorithms for constraint sets was 
above 63.97%. The highest decrease in normalized error after five iterations for 
the constraint set of 3900 was 70.31%, while the lowest decrease for the 
constraint set of 3000 was with 63.97%. Pearson correlation analysis between 
graph parameters and normalized error was carried out. We identified that graph 
parameters such as diameter, average eccentricity, global efficiency, and 
average local efficiency showed strong correlations to the normalized error.
CONCLUSIONS: We observed that iteration monotonically decreases the error in all 
experiments. Our iteration results showed decreased normalized error using the 
partitioned constrained optimization by linear approximation to the non-linear 
optimization model.

Copyright © 2020 Elsevier Ltd. All rights reserved.

DOI: 10.1016/j.compbiomed.2020.103695
PMCID: PMC7197414
PMID: 32339127 [Indexed for MEDLINE]

Conflict of interest statement: Declaration of competing interest The authors 
declare that they have no conflict of interest.